We use a highly localised resistive heating technique to grow vertically aligned multiwalled nanotube films and aligned single-walled nanotubes on substrates with an average temperature of less than 100oC. The temperature at the catalyst can easily be as high as 1000oC but an extremely high temperature gradient ensures that the surrounding chip is held at much lower temperatures, even as close as 1μm away from the local heater. We demonstrate the influence of temperature on the height of multi-walled nanotube films, illustrate the feasibility of sequential growth of single-walled nanotubes by switching between local heaters and also show that nanotubes can be grown over temperature sensitive materials such as resist polymer.